Abstract
We investigate how the laws of gravity change in the DGP model, if we add a second, parallel 3-brane, endowed with a localized gravitational curvature term. We calculate the gravitational potential energy between two static point sources localized on different branes. We discover a new length scale, which is equal to the geometric mean of the DGP cross-over scale and the separation of the two branes in the extra dimension. For distances, which are larger than this new length scale, we recover the original DGP result, but for smaller distances the gravitational potential is weaker. Furthermore, a region emerges, where a 4-dimensional observer measures a distance independent force. We discuss a possible application of the present scenario for deriving rotation curves of low surface brightness galaxies. Using the Kaluza-Klein description, we observe a curious pattern, in which even and odd KK-modes contribute to the attractive and repulsive parts of the gravitational potential, respectively. Finally, since this setup allows for the existence of a sector of particle species that are interacting arbitrarily weakly with “our” sector, we discuss the implications of this phenomenon for black holes and the bound on the number of species. We find that the behavior is qualitatively different from theories with a normalizable zero-mode graviton.
Highlights
Where y is the coordinate of the extra dimension, |G| is the determinant of the bulk metric, R5 is the bulk Ricci scalar and |g| (with gμν(xμ) = GAB(xμ, y = 0)) and R are the respective quantities on the brane
We find that a 2nd brane together with its induced kinetic term has no influence on gravity in our world, if the brane is far away
We have shown that the potential energy between two static point masses shows similar properties as in the original DGP-setup, but it acquires a qualitatively different behavior
Summary
As was explained in ref. [2], in order to see the essential features of the DGP scenario, it is enough to consider a toy model with a bulk scalar field and the respective kinetic term(s) localized on the brane(s). [2], in order to see the essential features of the DGP scenario, it is enough to consider a toy model with a bulk scalar field and the respective kinetic term(s) localized on the brane(s). The full theory, involving a spin-2 particle, will add a tensor-structure to the scalar field propagator, but the essential results of the present work will be unaffected.. We will consider the following scalar field theory: S=. M∗3 the so-called cross-over length scale, which quantifies the relative strengths of the scalar field propagators on the brane and the bulk, respectively. This simulates the relative strengths of the 4-d and the 5-d gravity in our toy model. We will perform the 5-d calculation, while we will integrate out the extra dimension and use the KK language
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
